There is known a boring head of a multiple-operation machine tool, comprising a housing which is kinematically coupled to a spindle and which accommodates a carriage carrying a mandrel for a cutting tool and has three slanted surfaces. One of the slanted surfaces is intended to interact with a slanted surface of a rod arranged in the housing coaxially with the latter, and kinematically coupled to a drive which moves the rod in the axial direction. The two other slanted surfaces are arranged symmetrically in relation to the axis of rotation of the boring head, and interact with rollers whose axles are perpendicular to the axis of rotation of the boring head and are mounted on the ends of a fork elastically pressed against the carriage. The fork is arranged in the housing coaxially with the latter. The rollers interact with the slanted surfaces on lines found on a plane extending through the axis of rotation of the boring head (cf. USSR Inventor's Certificate No. 665,994). The head in question does not provide for a high speed of response with regard to the rod motion; nor does it provide for a play-free motion of the carriage in the housing, because friction between the bearing surfaces of the fork and the housing bends the former. As a result, the fork may get jammed in the housing. Furthermore, the fork cannot properly position itself with respect to the two slanted surfaces of the carriage, which reduces the accuracy of machining and affects the efficiency of the machine tool.